Problem: The first three stages of a pattern are shown below, in which each line segment represents a toothpick. If the pattern continues such that at each successive stage, three toothpicks are added to the previous arrangement, how many toothpicks are necessary to create the arrangement for the 250th stage? [asy]
size(150);
defaultpen(linewidth(0.7));
void drawSquare(pair A){

draw((A.x + 0.1,A.y)--(A.x + 0.9,A.y));

draw((A.x,A.y + 0.1)--(A.x,A.y + 0.9));

draw((A.x + 1,A.y + 0.1)--(A.x + 1,A.y + 0.9));

draw((A.x + 0.1,A.y + 1)--(A.x + 0.9,A.y + 1));
}

int k = 0;

for(int i = 1; i <= 3; ++i){

for(int j = 0; j < i; ++j){

drawSquare((k,0));

++k;

}

draw((k+0.1,0.5)--(k+0.9,0.5),EndArrow);

++k;
}
label("$\cdots$",(k,0.5));
[/asy]
Answer: The number of toothpicks in each stage form an arithmetic sequence.  The first term in this arithmetic sequence is 4, and the common difference is 3 (the number of toothpicks added to get to the next stage), so the number of toothpicks used in the 250th stage is $4 + 3 \cdot 249 = \boxed{751}$.